{
  "abstract": "For $n\\in\\mathbb{N}$, we consider the set of lattice paths from $(0,0)$ to $(n,n)$ using only unit north and east steps. Given a point $B$ to be avoided, we ask: at which point $A$ on the grid with corners $(0,0)$ and $(n,n)$, different from the endpoints, does the largest number of $B$-avoiding lattice paths pass through? We show that for $n\\ge 9$, regardless of the location of $B$, the maximum is attained at one of ten specific points clustered near the two endpoints of the grid. This stability, however, conceals an interesting anomaly. When the obstruction $B$ lies on the antidiagonal $x+y=n$, the points of maximal traffic migrate from the near-corner points $(1,1)$ and $(n-1,n-1)$ to boundary points in the set of possible maximizers. The migration occurs for every $8\\le n\\le 375$, and intermittently up to $n=495$. We conjecture that the anomaly disappears for $n\\ge 496$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01562",
  "author_total": 4,
  "authors": [
    {
      "name": "Juan Gil"
    },
    {
      "name": "Zhenni Liang"
    },
    {
      "name": "Ayodeji Odetola"
    },
    {
      "name": "Michael Weiner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vzjskt0nxcys.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01562",
  "fulltext_url": null,
  "id": "7vzjskt0nxcys",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01562",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7206163366",
  "pdf_url": "https://arxiv.org/pdf/2609.01562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vzjskt0nxcys.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Points of maximal traffic on a grid with obstruction",
  "title_text": "Points of maximal traffic on a grid with obstruction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/7vzjskt0nxcys",
  "venue": "arXiv",
  "versions": []
}